Is the tube sticking out through a hole, or under the bead?
I just use my thumbs to mount the tire. However, when one gets to the last section, be careful to push the tube inside of the rim, rather than letting it roll on the side of the rim, and end up under the bead.
I always start at the valve stem, and work away. However, I've seen a video of a person working towards the valve, then giving the valve a little push to make sure it is loose. Theoretically this would help keep the tube in the tire.